Search

In this paper, we start by reviewing exchangeability and its relevance to the Bayesian approach. We highlight the predictive nature of Bayesian models and the symmetry assumptions implied by beliefs of an underlying exchangeable sequence of observations. By taking a closer look at the Bayesian bootstrap, the parametric bootstrap of Efron and a version of Bayesian thinking about inference uncovered by Doob based on martingales, we introduce a parametric Bayesian bootstrap. Martingales play a fundamental role. Illustrations are presented as is the relevant theory. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

Severe falciparum malaria has substantially affected human evolution. Genetic association studies of patients with clinically defined severe malaria and matched population controls have helped characterise human genetic susceptibility to severe malaria, but phenotypic imprecision compromises discovered associations. In areas of high malaria transmission, the diagnosis of severe malaria in young children and, in particular, the distinction from bacterial sepsis are imprecise. We developed a probabilistic diagnostic model of severe malaria using platelet and white count data. Under this model, we re-analysed clinical and genetic data from 2220 Kenyan children with clinically defined severe malaria and 3940 population controls, adjusting for phenotype mis-labelling. Our model, validated by the distribution of sickle trait, estimated that approximately one-third of cases did not have severe malaria. We propose a data-tilting approach for case-control studies with phenotype mis-labelling and show that this reduces false discovery rates and improves statistical power in genome-wide association studies., Competing Interests: JW, CN, SU, AM, GN, SM, CN, NM, NP, BT, KR, SL, HK, EG, KM, ND, AD, PB, TW, CH, NW No competing interests declared, (© 2021, Watson et al.)

Genetic surveillance of malaria parasites supports malaria control programmes, treatment guidelines and elimination strategies. Surveillance studies often pose questions about malaria parasite ancestry (e.g. how antimalarial resistance has spread) and employ statistical methods that characterise parasite population structure. Many of the methods used to characterise structure are unsupervised machine learning algorithms which depend on a genetic distance matrix, notably principal coordinates analysis (PCoA) and hierarchical agglomerative clustering (HAC). PCoA and HAC are sensitive to both the definition of genetic distance and algorithmic specification. Importantly, neither algorithm infers malaria parasite ancestry. As such, PCoA and HAC can inform (e.g. via exploratory data visualisation and hypothesis generation), but not answer comprehensively, key questions about malaria parasite ancestry. We illustrate the sensitivity of PCoA and HAC using 393 Plasmodium falciparum whole genome sequences collected from Cambodia and neighbouring regions (where antimalarial resistance has emerged and spread recently) and we provide tentative guidance for the use and interpretation of PCoA and HAC in malaria parasite genetic epidemiology. This guidance includes a call for fully transparent and reproducible analysis pipelines that feature (i) a clearly outlined scientific question; (ii) a clear justification of analytical methods used to answer the scientific question along with discussion of any inferential limitations; (iii) publicly available genetic distance matrices when downstream analyses depend on them; and (iv) sensitivity analyses. To bridge the inferential disconnect between the output of non-inferential unsupervised learning algorithms and the scientific questions of interest, tailor-made statistical models are needed to infer malaria parasite ancestry. In the absence of such models speculative reasoning should feature only as discussion but not as results., Competing Interests: The authors have declared that no competing interests exist.

Background: Exploration and modelling of heterogeneous treatment effects as a function of baseline covariates is an important aspect of precision medicine in randomised controlled trials (RCTs). Randomisation generally guarantees the internal validity of an RCT, but heterogeneity in treatment effect can reduce external validity. Estimation of heterogeneous treatment effects is usually done via a predictive model for individual outcomes, where one searches for interactions between treatment allocation and important patient baseline covariates. However, such models are prone to overfitting and multiple testing and typically demand a transformation of the outcome measurement, for example, from the absolute risk in the original RCT to log-odds of risk in the predictive model., Methods: We show how reference classes derived from baseline covariates can be used to explore heterogeneous treatment effects via a two-stage approach. We first estimate a risk score which captures on a single dimension some of the heterogeneity in outcomes of the trial population. Heterogeneity in the treatment effect can then be explored via reweighting schemes along this axis of variation. This two-stage approach bypasses the search for interactions with multiple covariates, thus protecting against multiple testing. It also allows for exploration of heterogeneous treatment effects on the original outcome scale of the RCT. This approach would typically be applied to multivariable models of baseline risk to assess the stability of average treatment effects with respect to the distribution of risk in the population studied., Case Study: We illustrate this approach using the single largest randomised treatment trial in severe falciparum malaria and demonstrate how the estimated treatment effect in terms of absolute mortality risk reduction increases considerably in higher risk strata., Conclusions: 'Local' and 'tilting' reweighting schemes based on ranking patients by baseline risk can be used as a general approach for exploring, graphing and reporting heterogeneity of treatment effect in RCTs., Trial Registration: ISRCTN clinical trials registry: ISRCTN50258054. Prospectively registered on 22 July 2005.

Puberty is the most important developmental milestone closely preceding a young adult's labor market decisions. Thus, we examine the variation in the timing of physical maturity during adolescence to isolate its association with employment and hourly wages for US young adults. Using the National Longitudinal Study of Adolescent to Adult Health data, we find an early maturity premium of about 6% for females and 8% for males, but no employment advantage, in excess of gains from height and physical attractiveness. Cognitive and personality factors significantly explain this premium for both genders, but job attributes are also important for males., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Background: Retrospective exploratory analyses of randomised controlled trials (RCTs) seeking to identify treatment effect heterogeneity (TEH) are prone to bias and false positives. Yet the desire to learn all we can from exhaustive data measurements on trial participants motivates the inclusion of such analyses within RCTs. Moreover, widespread advances in machine learning (ML) methods hold potential to utilise such data to identify subjects exhibiting heterogeneous treatment response., Methods: We present a novel analysis strategy for detecting TEH in randomised data using ML methods, whilst ensuring proper control of the false positive discovery rate. Our approach uses random data partitioning with statistical or ML-based prediction on held-out data. This method can test for both crossover TEH (switch in optimal treatment) and non-crossover TEH (systematic variation in benefit across patients). The former is done via a two-sample hypothesis test measuring overall predictive performance. The latter is done via 'stacking' the ML predictors alongside a classical statistical model to formally test the added benefit of the ML algorithm. An adaptation of recent statistical theory allows for the construction of a valid aggregate p value. This testing strategy is independent of the choice of ML method., Results: We demonstrate our approach with a re-analysis of the SEAQUAMAT trial, which compared quinine to artesunate for the treatment of severe malaria in Asian adults. We find no evidence for any subgroup who would benefit from a change in treatment from the current standard of care, artesunate, but strong evidence for significant TEH within the artesunate treatment group. In particular, we find that artesunate provides a differential benefit to patients with high numbers of circulating ring stage parasites., Conclusions: ML analysis plans using computational notebooks (documents linked to a programming language that capture the model parameter settings, data processing choices, and evaluation criteria) along with version control can improve the robustness and transparency of RCT exploratory analyses. A data-partitioning algorithm allows researchers to apply the latest ML techniques safe in the knowledge that any declared associations are statistically significant at a user-defined level.

Transcriptome deconvolution in cancer and other heterogeneous tissues remains challenging. Available methods lack the ability to estimate both component-specific proportions and expression profiles for individual samples. We present DeMixT, a new tool to deconvolve high-dimensional data from mixtures of more than two components. DeMixT implements an iterated conditional mode algorithm and a novel gene-set-based component merging approach to improve accuracy. In a series of experimental validation studies and application to TCGA data, DeMixT showed high accuracy. Improved deconvolution is an important step toward linking tumor transcriptomic data with clinical outcomes. An R package, scripts, and data are available: https://github.com/wwylab/DeMixTallmaterials., (Published by Elsevier Inc.)

We are entering a new era of mouse phenomics, driven by large-scale and economical generation of mouse mutants coupled with increasingly sophisticated and comprehensive phenotyping. These studies are generating large, multidimensional gene-phenotype data sets, which are shedding new light on the mammalian genome landscape and revealing many hitherto unknown features of mammalian gene function. Moreover, these phenome resources provide a wealth of disease models and can be integrated with human genomics data as a powerful approach for the interpretation of human genetic variation and its relationship to disease. In the future, the development of novel phenotyping platforms allied to improved computational approaches, including machine learning, for the analysis of phenotype data will continue to enhance our ability to develop a comprehensive and powerful model of mammalian gene-phenotype space.

In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a "null model" of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets.

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.

Background: Altered sensitivity to multiple antimalarial drugs is mediated by polymorphisms in pfmdr1 , which encodes the Plasmodium falciparum multidrug resistance transporter. In Africa the N86Y and D1246Y polymorphisms have been shown to be selected by treatment, with artemether-lumefantrine (AL) and dihydroartemisinin-piperaquine (DP) selecting for wild-type and mutant alleles, respectively. However, there has been little study of pfmdr1 haplotypes, in part because haplotype analyses are complicated by multiclonal infections., Methods: We fit a haplotype frequency estimation model, which accounts for multiclonal infections, to the polymorphic pfmdr1 N86Y, Y184F, and D1246Y alleles in samples from a longitudinal trial comparing AL and DP to treat uncomplicated P falciparum malaria in Tororo, Uganda from 2007 to 2012. We regressed estimates onto covariates of trial arm and selective drug pressure., Results: Yearly trends showed increasing frequency estimates for haplotypes with wild type pfmdr1 N86 and D1246 alleles and decreasing frequency estimates for haplotypes with the mutant pfmdr1 86Y allele. Considering days since prior therapy, we saw evidence suggestive of selection by AL for haplotypes with N86 combined with 184F, D1246, or both, and against all haplotypes with 86Y, and evidence suggestive of selection by DP for 86Y only when combined with Y184 and 1246Y (haplotype YYY) and against haplotypes NFD and NYY., Conclusions: Based on our model, AL selected several haplotypes containing N86, whereas DP selection was haplotype specific, demonstrating the importance of haplotype analyses. Inverse selective pressure of AL and DP on the complementary haplotypes NFD and YYY suggests that rotating artemisinin-based antimalarial combination regimens may be the best treatment option to prevent resistance selection.

We present a novel Bayesian nonparametric regression model for covariates X and continuous response variable Y ∈ ℝ. The model is parametrized in terms of marginal distributions for Y and X and a regression function which tunes the stochastic ordering of the conditional distributions F ( y|x ). By adopting an approximate composite likelihood approach, we show that the resulting posterior inference can be decoupled for the separate components of the model. This procedure can scale to very large datasets and allows for the use of standard, existing, software from Bayesian nonparametric density estimation and Plackett-Luce ranking estimation to be applied. As an illustration, we show an application of our approach to a US Census dataset, with over 1,300,000 data points and more than 100 covariates.

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward-backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k -segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k -segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online.

Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.

Upper- and lower-body fat depots exhibit opposing associations with obesity-related metabolic disease. We defined the relationship between DEXA-quantified fat depots and diabetes/cardiovascular risk factors in a healthy population-based cohort (n = 3,399). Gynoid fat mass correlated negatively with insulin resistance after total fat mass adjustment, whereas the opposite was seen for abdominal fat. Paired transcriptomic analysis of gluteal subcutaneous adipose tissue (GSAT) and abdominal subcutaneous adipose tissue (ASAT) was performed across the BMI spectrum (n = 49; 21.4-45.5 kg/m(2)). In both depots, energy-generating metabolic genes were negatively associated and inflammatory genes were positively associated with obesity. However, associations were significantly weaker in GSAT. At the systemic level, arteriovenous release of the proinflammatory cytokine interleukin-6 (n = 34) was lower from GSAT than ASAT. Isolated preadipocytes retained a depot-specific transcriptional "memory" of embryonic developmental genes and exhibited differential promoter DNA methylation of selected genes (HOTAIR, TBX5) between GSAT and ASAT. Short hairpin RNA-mediated silencing identified TBX5 as a regulator of preadipocyte proliferation and adipogenic differentiation in ASAT. In conclusion, intrinsic differences in the expression of developmental genes in regional adipocytes provide a mechanistic basis for diversity in adipose tissue (AT) function. The less inflammatory nature of lower-body AT offers insight into the opposing metabolic disease risk associations between upper- and lower-body obesity., (© 2014 by the American Diabetes Association. Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered.)

Background: Reliable measures of anti-malarial resistance are crucial for malaria control. Resistance is typically a complex trait: multiple mutations in a single parasite (a haplotype or genotype) are necessary for elaboration of the resistant phenotype. The frequency of a genetic motif (proportion of parasite clones in the parasite population that carry a given allele, haplotype or genotype) is a useful measure of resistance. In areas of high endemicity, malaria patients generally harbour multiple parasite clones; they have multiplicities of infection (MOIs) greater than one. However, most standard experimental procedures only allow measurement of marker prevalence (proportion of patient blood samples that test positive for a given mutation or combination of mutations), not frequency. It is misleading to compare marker prevalence between sites that have different mean MOIs; frequencies are required instead., Methods: A Bayesian statistical model was developed to estimate Plasmodium falciparum genetic motif frequencies from prevalence data collected in the field. To assess model performance and computational speed, a detailed simulation study was implemented. Application of the model was tested using datasets from five sites in Uganda. The datasets included prevalence data on markers of resistance to sulphadoxine-pyrimethamine and an average MOI estimate for each study site., Results: The simulation study revealed that the genetic motif frequencies that were estimated using the model were more accurate and precise than conventional estimates based on direct counting. Importantly, the model did not require measurements of the MOI in each patient; it used the average MOI in the patient population. Furthermore, if a dataset included partially genotyped patient blood samples, the model imputed the data that were missing. Using the model and the Ugandan data, genotype frequencies were estimated and four biologically relevant genotypes were identified., Conclusions: The model allows fast, accurate, reliable estimation of the frequency of genetic motifs associated with resistance to anti-malarials using prevalence data collected from malaria patients. The model does not require per-patient MOI measurements and can easily analyse data from five markers. The model will be a valuable tool for monitoring markers of anti-malarial drug resistance, including markers of resistance to artemisinin derivatives and partner drugs.

Objectives: Microsatellite instability (MSI) is an established marker of good prognosis in colorectal cancer (CRC). Chromosomal instability (CIN) is strongly negatively associated with MSI and has been shown to be a marker of poor prognosis in a small number of studies. However, a substantial group of "double-negative" (MSI-/CIN-) CRCs exists. The prognosis of these patients is unclear. Furthermore, MSI and CIN are each associated with specific molecular changes, such as mutations in KRAS and BRAF, that have been associated with prognosis. It is not known which of MSI, CIN, and the specific gene mutations are primary predictors of survival., Methods: We evaluated the prognostic value (disease-free survival, DFS) of CIN, MSI, mutations in KRAS, NRAS, BRAF, PIK3CA, FBXW7, and TP53, and chromosome 18q loss-of-heterozygosity (LOH) in 822 patients from the VICTOR trial of stage II/III CRC. We followed up promising associations in an Australian community-based cohort (N=375)., Results: In the VICTOR patients, no specific mutation was associated with DFS, but individually MSI and CIN showed significant associations after adjusting for stage, age, gender, tumor location, and therapy. A combined analysis of the VICTOR and community-based cohorts showed that MSI and CIN were independent predictors of DFS (for MSI, hazard ratio (HR)=0.58, 95% confidence interval (CI) 0.36-0.93, and P=0.021; for CIN, HR=1.54, 95% CI 1.14-2.08, and P=0.005), and joint CIN/MSI testing significantly improved the prognostic prediction of MSI alone (P=0.028). Higher levels of CIN were monotonically associated with progressively poorer DFS, and a semi-quantitative measure of CIN was a better predictor of outcome than a simple CIN+/- variable. All measures of CIN predicted DFS better than the recently described Watanabe LOH ratio., Conclusions: MSI and CIN are independent predictors of DFS for stage II/III CRC. Prognostic molecular tests for CRC relapse should currently use MSI and a quantitative measure of CIN rather than specific gene mutations.

Motivation: The identification of nucleosomes along the chromatin is key to understanding their role in the regulation of gene expression and other DNA-related processes. However, current experimental methods (MNase-ChIP, MNase-Seq) sample nucleosome positions from a cell population and contain biases, making thus the precise identification of individual nucleosomes not straightforward. Recent works have only focused on the first point, where noise reduction approaches have been developed to identify nucleosome positions., Results: In this article, we propose a new approach, termed NucleoFinder, that addresses both the positional heterogeneity across cells and experimental biases by seeking nucleosomes consistently positioned in a cell population and showing a significant enrichment relative to a control sample. Despite the absence of validated dataset, we show that our approach (i) detects fewer false positives than two other nucleosome calling methods and (ii) identifies two important features of the nucleosome organization (the nucleosome spacing downstream of active promoters and the enrichment/depletion of GC/AT dinucleotides at the centre of in vitro nucleosomes) with equal or greater ability than the other two methods.

Many individuals with multiple or large colorectal adenomas or early-onset colorectal cancer (CRC) have no detectable germline mutations in the known cancer predisposition genes. Using whole-genome sequencing, supplemented by linkage and association analysis, we identified specific heterozygous POLE or POLD1 germline variants in several multiple-adenoma and/or CRC cases but in no controls. The variants associated with susceptibility, POLE p.Leu424Val and POLD1 p.Ser478Asn, have high penetrance, and POLD1 mutation was also associated with endometrial cancer predisposition. The mutations map to equivalent sites in the proofreading (exonuclease) domain of DNA polymerases ɛ and δ and are predicted to cause a defect in the correction of mispaired bases inserted during DNA replication. In agreement with this prediction, the tumors from mutation carriers were microsatellite stable but tended to acquire base substitution mutations, as confirmed by yeast functional assays. Further analysis of published data showed that the recently described group of hypermutant, microsatellite-stable CRCs is likely to be caused by somatic POLE mutations affecting the exonuclease domain.

Background: In order to better understand cancer as a complex disease with multiple genetic and epigenetic factors, it is vital to model the fundamental biological relationships among these alterations as well as their relationships with important clinical outcomes., Methods: We develop an integrative network-based Bayesian analysis (iNET) approach that allows us to jointly analyze multi-platform high-dimensional genomic data in a computationally efficient manner. The iNET approach is formulated as an objective Bayesian model selection problem for Gaussian graphical models to model joint dependencies among platform-specific features using known biological mechanisms. Using both simulated datasets and a glioblastoma (GBM) study from The Cancer Genome Atlas (TCGA), we illustrate the iNET approach via integrating three data types, microRNA, gene expression (mRNA), and patient survival time., Results: We show that the iNET approach has greater power in identifying cancer-related microRNAs than non-integrative approaches based on realistic simulated datasets. In the TCGA GBM study, we found many mRNA-microRNA pairs and microRNAs that are associated with patient survival time, with some of these associations identified in previous studies., Conclusions: The iNET discovers relationships consistent with the underlying biological mechanisms among these variables, as well as identifying important biomarkers that are potentially relevant to patient survival. In addition, we identified some microRNAs that can potentially affect patient survival which are missed by non-integrative approaches.

The stochastic nature of generating eukaryotic transcripts challenges conventional methods for obtaining and analyzing single-cell gene expression data. In order to address the inherent noise, detailed methods are described on how to collect data on multiple genes in a large number of single cells using microfluidic arrays. As part of a study exploring the effect of genotype on Wnt pathway activation, data were collected for 96 qPCR assays on 1440 lymphoblastoid cells. The description of methods includes preliminary data processing steps. The methods used in the collection and analysis of single-cell qPCR data are contrasted with those used in conventional qPCR., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Summary: GREVE has been developed to assist with the identification of recurrent genomic aberrations across cancer samples. The exact characterization of such aberrations remains a challenge despite the availability of increasing amount of data, from SNParray to next-generation sequencing. Furthermore, genomic aberrations in cancer are especially difficult to handle because they are, by nature, unique to the patients. However, their recurrence in specific regions of the genome has been shown to reflect their relevance in the development of tumors. GREVE makes use of previously characterized events to identify such regions and focus any further analysis., Availability: GREVE is available through a web interface and open-source application (http://www.well.ox.ac.uk/GREVE).

Significance testing one SNP at a time has proven useful for identifying genomic regions that harbor variants affecting human disease. But after an initial genome scan has identified a "hit region" of association, single-locus approaches can falter. Local linkage disequilibrium (LD) can make both the number of underlying true signals and their identities ambiguous. Simultaneous modeling of multiple loci should help. However, it is typically applied ad hoc: conditioning on the top SNPs, with limited exploration of the model space and no assessment of how sensitive model choice was to sampling variability. Formal alternatives exist but are seldom used. Bayesian variable selection is coherent but requires specifying a full joint model, including priors on parameters and the model space. Penalized regression methods (e.g., LASSO) appear promising but require calibration, and, once calibrated, lead to a choice of SNPs that can be misleadingly decisive. We present a general method for characterizing uncertainty in model choice that is tailored to reprioritizing SNPs within a hit region under strong LD. Our method, LASSO local automatic regularization resample model averaging (LLARRMA), combines LASSO shrinkage with resample model averaging and multiple imputation, estimating for each SNP the probability that it would be included in a multi-SNP model in alternative realizations of the data. We apply LLARRMA to simulations based on case-control genome-wide association studies data, and find that when there are several causal loci and strong LD, LLARRMA identifies a set of candidates that is enriched for true signals relative to single locus analysis and to the recently proposed method of Stability Selection., (© 2012 Wiley Periodicals, Inc.)

Genome-wide array approaches and sequencing analyses are powerful tools for identifying genetic aberrations in cancers, including leukemias and lymphomas. However, the clinical and biological significance of such aberrations and their subclonal distribution are poorly understood. Here, we present the first genome-wide array based study of pre-treatment and relapse samples from patients with B-cell chronic lymphocytic leukemia (B-CLL) that uses the computational statistical tool OncoSNP. We show that quantification of the proportion of copy number alterations (CNAs) and copy neutral loss of heterozygosity regions (cnLOHs) in each sample is feasible. Furthermore, we (i) reveal complex changes in the subclonal architecture of paired samples at relapse compared with pre-treatment, (ii) provide evidence supporting an association between increased genomic complexity and poor clinical outcome (iii) report previously undefined, recurrent CNA/cnLOH regions that expand or newly occur at relapse and therefore might harbor candidate driver genes of relapse and/or chemotherapy resistance. Our findings are likely to impact on future therapeutic strategies aimed towards selecting effective and individually tailored targeted therapies.

Genome-wide association study (GWAS) data on a disease are increasingly available from multiple related populations. In this scenario, meta-analyses can improve power to detect homogeneous genetic associations, but if there exist ancestry-specific effects, via interactions on genetic background or with a causal effect that co-varies with genetic background, then these will typically be obscured. To address this issue, we have developed a robust statistical method for detecting susceptibility gene-ancestry interactions in multi-cohort GWAS based on closely-related populations. We use the leading principal components of the empirical genotype matrix to cluster individuals into "ancestry groups" and then look for evidence of heterogeneous genetic associations with disease or other trait across these clusters. Robustness is improved when there are multiple cohorts, as the signal from true gene-ancestry interactions can then be distinguished from gene-collection artefacts by comparing the observed interaction effect sizes in collection groups relative to ancestry groups. When applied to colorectal cancer, we identified a missense polymorphism in iron-absorption gene CYBRD1 that associated with disease in individuals of English, but not Scottish, ancestry. The association replicated in two additional, independently-collected data sets. Our method can be used to detect associations between genetic variants and disease that have been obscured by population genetic heterogeneity. It can be readily extended to the identification of genetic interactions on other covariates such as measured environmental exposures. We envisage our methodology being of particular interest to researchers with existing GWAS data, as ancestry groups can be easily defined and thus tested for interactions.

Metabolic Syndrome (MetS) is highly prevalent and has considerable public health impact, but its underlying genetic factors remain elusive. To identify gene networks involved in MetS, we conducted whole-genome expression and genotype profiling on abdominal (ABD) and gluteal (GLU) adipose tissue, and whole blood (WB), from 29 MetS cases and 44 controls. Co-expression network analysis for each tissue independently identified nine, six, and zero MetS-associated modules of coexpressed genes in ABD, GLU, and WB, respectively. Of 8,992 probesets expressed in ABD or GLU, 685 (7.6%) were expressed in ABD and 51 (0.6%) in GLU only. Differential eigengene network analysis of 8,256 shared probesets detected 22 shared modules with high preservation across adipose depots (D(ABD-GLU) = 0.89), seven of which were associated with MetS (FDR P<0.01). The strongest associated module, significantly enriched for immune response-related processes, contained 94/620 (15%) genes with inter-depot differences. In an independent cohort of 145/141 twins with ABD and WB longitudinal expression data, median variability in ABD due to familiality was greater for MetS-associated versus un-associated modules (ABD: 0.48 versus 0.18, P = 0.08; GLU: 0.54 versus 0.20, P = 7.8×10(-4)). Cis-eQTL analysis of probesets associated with MetS (FDR P<0.01) and/or inter-depot differences (FDR P<0.01) provided evidence for 32 eQTLs. Corresponding eSNPs were tested for association with MetS-related phenotypes in two GWAS of >100,000 individuals; rs10282458, affecting expression of RARRES2 (encoding chemerin), was associated with body mass index (BMI) (P = 6.0×10(-4)); and rs2395185, affecting inter-depot differences of HLA-DRB1 expression, was associated with high-density lipoprotein (P = 8.7×10(-4)) and BMI-adjusted waist-to-hip ratio (P = 2.4×10(-4)). Since many genes and their interactions influence complex traits such as MetS, integrated analysis of genotypes and coexpression networks across multiple tissues relevant to clinical traits is an efficient strategy to identify novel associations., Competing Interests: The authors have declared that no competing interests exist.

In biomarker discovery studies, uncertainty associated with case and control labels is often overlooked. By omitting to take into account label uncertainty, model parameters and the predictive risk can become biased, sometimes severely. The most common situation is when the control set contains an unknown number of undiagnosed, or future, cases. This has a marked impact in situations where the model needs to be well-calibrated, e.g., when the prediction performance of a biomarker panel is evaluated. Failing to account for class label uncertainty may lead to underestimation of classification performance and bias in parameter estimates. This can further impact on meta-analysis for combining evidence from multiple studies. Using a simulation study, we outline how conventional statistical models can be modified to address class label uncertainty leading to well-calibrated prediction performance estimates and reduced bias in meta-analysis. We focus on the problem of mislabeled control subjects in case-control studies, i.e., when some of the control subjects are undiagnosed cases, although the procedures we report are generic. The uncertainty in control status is a particular situation common in biomarker discovery studies in the context of genomic and molecular epidemiology, where control subjects are commonly sampled from the general population with an established expected disease incidence rate.

Background: The advent of affinity-based proteomics technologies for global protein profiling provides the prospect of finding new molecular biomarkers for common, multifactorial disorders. The molecular phenotypes obtained from studies on such platforms are driven by multiple sources, including genetic, environmental, and experimental components. In characterizing the contribution of different sources of variation to the measured phenotypes, the aim is to facilitate the design and interpretation of future biomedical studies employing exploratory and multiplexed technologies. Thus, biometrical genetic modelling of twin or other family data can be used to decompose the variation underlying a phenotype into biological and experimental components., Results: Using antibody suspension bead arrays and antibodies from the Human Protein Atlas, we study unfractionated serum from a longitudinal study on 154 twins. In this study, we provide a detailed description of how the variation in a molecular phenotype in terms of protein profile can be decomposed into familial i.e. genetic and common environmental; individual environmental, short-term biological and experimental components. The results show that across 69 antibodies analyzed in the study, the median proportion of the total variation explained by familial sources is 12% (IQR 1-22%), and the median proportion of the total variation attributable to experimental sources is 63% (IQR 53-72%)., Conclusion: The variability analysis of antibody arrays highlights the importance to consider variability components and their relative contributions when designing and evaluating studies for biomarker discoveries with exploratory, high-throughput and multiplexed methods.

We have performed a metabolite quantitative trait locus (mQTL) study of the (1)H nuclear magnetic resonance spectroscopy ((1)H NMR) metabolome in humans, building on recent targeted knowledge of genetic drivers of metabolic regulation. Urine and plasma samples were collected from two cohorts of individuals of European descent, with one cohort comprised of female twins donating samples longitudinally. Sample metabolite concentrations were quantified by (1)H NMR and tested for association with genome-wide single-nucleotide polymorphisms (SNPs). Four metabolites' concentrations exhibited significant, replicable association with SNP variation (8.6×10(-11)

¹H Nuclear Magnetic Resonance spectroscopy (¹H NMR) is increasingly used to measure metabolite concentrations in sets of biological samples for top-down systems biology and molecular epidemiology. For such purposes, knowledge of the sources of human variation in metabolite concentrations is valuable, but currently sparse. We conducted and analysed a study to create such a resource. In our unique design, identical and non-identical twin pairs donated plasma and urine samples longitudinally. We acquired ¹H NMR spectra on the samples, and statistically decomposed variation in metabolite concentration into familial (genetic and common-environmental), individual-environmental, and longitudinally unstable components. We estimate that stable variation, comprising familial and individual-environmental factors, accounts on average for 60% (plasma) and 47% (urine) of biological variation in ¹H NMR-detectable metabolite concentrations. Clinically predictive metabolic variation is likely nested within this stable component, so our results have implications for the effective design of biomarker-discovery studies. We provide a power-calculation method which reveals that sample sizes of a few thousand should offer sufficient statistical precision to detect ¹H NMR-based biomarkers quantifying predisposition to disease.

To understand how miRNAs contribute to the molecular phenotype of adipose tissues and related traits, we performed global miRNA expression profiling in subcutaneous abdominal and gluteal adipose tissue of 70 human subjects and characterised which miRNAs were differentially expressed between these tissues. We found that 12% of the miRNAs were significantly differentially expressed between abdominal and gluteal adipose tissue (FDR adjusted p<0.05) in the primary study, of which 59 replicated in a follow-up study of 40 additional subjects. Further, 14 miRNAs were found to be associated with metabolic syndrome case-control status in abdominal tissue and three of these replicated (primary study: FDR adjusted p<0.05, replication: p<0.05 and directionally consistent effect). Genome-wide genotyping was performed in the 70 subjects to enable miRNA expression quantitative trait loci (eQTL) analysis. Candidate miRNA eQTLs were followed-up in the additional 40 subjects and six significant, independent cis-located miRNA eQTLs (primary study: p<0.001; replication: p<0.05 and directionally consistent effect) were identified. Finally, global mRNA expression profiling was performed in both tissues to enable association analysis between miRNA and target mRNA expression levels. We find 22% miRNAs in abdominal and 9% miRNAs in gluteal adipose tissue with expression levels significantly associated with the expression of corresponding target mRNAs (FDR adjusted p<0.05). Taken together, our results indicate a clear difference in the miRNA molecular phenotypic profile of abdominal and gluteal adipose tissue, that the expressions of some miRNAs are influenced by cis-located genetic variants and that miRNAs are associated with expression levels of their predicted mRNA targets.

We present a case-study on the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods. Graphics cards, containing multiple Graphics Processing Units (GPUs), are self-contained parallel computational devices that can be housed in conventional desktop and laptop computers and can be thought of as prototypes of the next generation of many-core processors. For certain classes of population-based Monte Carlo algorithms they offer massively parallel simulation, with the added advantage over conventional distributed multi-core processors that they are cheap, easily accessible, easy to maintain, easy to code, dedicated local devices with low power consumption. On a canonical set of stochastic simulation examples including population-based Markov chain Monte Carlo methods and Sequential Monte Carlo methods, we nd speedups from 35 to 500 fold over conventional single-threaded computer code. Our findings suggest that GPUs have the potential to facilitate the growth of statistical modelling into complex data rich domains through the availability of cheap and accessible many-core computation. We believe the speedup we observe should motivate wider use of parallelizable simulation methods and greater methodological attention to their design.

Waist-hip ratio (WHR) is a measure of body fat distribution and a predictor of metabolic consequences independent of overall adiposity. WHR is heritable, but few genetic variants influencing this trait have been identified. We conducted a meta-analysis of 32 genome-wide association studies for WHR adjusted for body mass index (comprising up to 77,167 participants), following up 16 loci in an additional 29 studies (comprising up to 113,636 subjects). We identified 13 new loci in or near RSPO3, VEGFA, TBX15-WARS2, NFE2L3, GRB14, DNM3-PIGC, ITPR2-SSPN, LY86, HOXC13, ADAMTS9, ZNRF3-KREMEN1, NISCH-STAB1 and CPEB4 (P = 1.9 × 10⁻⁹ to P = 1.8 × 10⁻⁴⁰) and the known signal at LYPLAL1. Seven of these loci exhibited marked sexual dimorphism, all with a stronger effect on WHR in women than men (P for sex difference = 1.9 × 10⁻³ to P = 1.2 × 10⁻¹³). These findings provide evidence for multiple loci that modulate body fat distribution independent of overall adiposity and reveal strong gene-by-sex interactions.

Motivation: Quantifying differences in linkage disequilibrium (LD) between sub-groups can highlight genetic regions or sites under selection and/or associated with disease, and may have utility in trans-ethnic mapping studies., Results: We present a novel pseudo Bayes factor (PBF) approach that assess differences in covariance of genotype frequencies from single nucleotide polymorphism (SNP) data from a genome-wide study. The magnitude of the PBF reflects the strength of evidence for a difference, while accounting for the sample size and number of SNPs, without the requirement for permutation testing to establish statistical significance. Application of the PBF to HapMap and Gambian malaria SNP data reveals regional LD differences, some known to be under selection., Availability and Implementation: The PBF approach has been implemented in the BALD (Bayesian analysis of LD differences) C++ software, and is available from http://homepages.lshtm.ac.uk/tgclark/downloads.

Standard techniques for single marker quantitative trait mapping perform poorly in detecting complex interacting genetic influences. When a genetic marker interacts with other genetic markers and/or environmental factors to influence a quantitative trait, a sample of individuals will show different effects according to their exposure to other interacting factors. This paper presents a Bayesian mixture model, which effectively models heterogeneous genetic effects apparent at a single marker. We compute approximate Bayes factors which provide an efficient strategy for screening genetic markers (genome-wide) for evidence of a heterogeneous effect on a quantitative trait. We present a simulation study which demonstrates that the approximation is good and provide a real data example which identifies a population-specific genetic effect on gene expression in the HapMap CEU and YRI populations. We advocate the use of the model as a strategy for identifying candidate interacting markers without any knowledge of the nature or order of the interaction. The source of heterogeneity can be modeled as an extension., ((c) 2009 Wiley-Liss, Inc.)

We describe a statistical method for the characterization of genomic aberrations in single nucleotide polymorphism microarray data acquired from cancer genomes. Our approach allows us to model the joint effect of polyploidy, normal DNA contamination and intra-tumour heterogeneity within a single unified Bayesian framework. We demonstrate the efficacy of our method on numerous datasets including laboratory generated mixtures of normal-cancer cell lines and real primary tumours.

Motivation: Identifying the network structure through which genes and their products interact can help to elucidate normal cell physiology as well as the genetic architecture of pathological phenotypes. Recently, a number of gene network inference tools have appeared based on Gaussian graphical model representations. Following this, we introduce a novel Boosting approach to learn the structure of a high-dimensional Gaussian graphical model motivated by the applications in genomics. A particular emphasis is paid to the inclusion of partial prior knowledge on the structure of the graph. With the increasing availability of pathway information and large-scale gene expression datasets, we believe that conditioning on prior knowledge will be an important aspect in raising the statistical power of structural learning algorithms to infer true conditional dependencies., Results: Our Boosting approach, termed BoostiGraph, is conceptually and algorithmically simple. It complements recent work on the network inference problem based on Lasso-type approaches. BoostiGraph is computationally cheap and is applicable to very high-dimensional graphs. For example, on graphs of order 5000 nodes, it is able to map out paths for the conditional independence structure in few minutes. Using computer simulations, we investigate the ability of our method with and without prior information to infer Gaussian graphical models from artificial as well as actual microarray datasets. The experimental results demonstrate that, using our method, it is possible to recover the true network topology with relatively high accuracy., Availability: This method and all other associated files are freely available from http://www.stats.ox.ac.uk/~anjum/.

Highly recombinant populations derived from inbred lines, such as advanced intercross lines and heterogeneous stocks, can be used to map loci far more accurately than is possible with standard intercrosses. However, the varying degrees of relatedness that exist between individuals complicate analysis, potentially leading to many false positive signals. We describe a method to deal with these problems that does not require pedigree information and accounts for model uncertainty through model averaging. In our method, we select multiple quantitative trait loci (QTL) models using forward selection applied to resampled data sets obtained by nonparametric bootstrapping and subsampling. We provide model-averaged statistics about the probability of loci or of multilocus regions being included in model selection, and this leads to more accurate identification of QTL than by single-locus mapping. The generality of our approach means it can potentially be applied to any population of unknown structure.

We have cultured Plasmodium falciparum directly from the blood of infected individuals to examine patterns of mature-stage gene expression in patient isolates. Analysis of the transcriptome of P. falciparum is complicated by the highly periodic nature of gene expression because small variations in the stage of parasite development between samples can lead to an apparent difference in gene expression values. To address this issue, we have developed statistical likelihood-based methods to estimate cell cycle progression and commitment to asexual or sexual development lineages in our samples based on microscopy and gene expression patterns. In cases subsequently matched for temporal development, we find that transcriptional patterns in ex vivo culture display little variation across patients with diverse clinical profiles and closely resemble transcriptional profiles that occur in vitro. These statistical methods, available to the research community, assist in the design and interpretation of P. falciparum expression profiling experiments where it is difficult to separate true differential expression from cell-cycle dependent expression. We reanalyze an existing dataset of in vivo patient expression profiles and conclude that previously observed discrete variation is consistent with the commitment of a varying proportion of the parasite population to the sexual development lineage.

Motivation: Conventional phylogenetic analysis for characterizing the relatedness between taxa typically assumes that a single relationship exists between species at every site along the genome. This assumption fails to take into account recombination which is a fundamental process for generating diversity and can lead to spurious results. Recombination induces a localized phylogenetic structure which may vary along the genome. Here, we generalize a hidden Markov model (HMM) to infer changes in phylogeny along multiple sequence alignments while accounting for rate heterogeneity; the hidden states refer to the unobserved phylogenic topology underlying the relatedness at a genomic location. The dimensionality of the number of hidden states (topologies) and their structure are random (not known a priori) and are sampled using Markov chain Monte Carlo algorithms. The HMM structure allows us to analytically integrate out over all possible changepoints in topologies as well as all the unknown branch lengths., Results: We demonstrate our approach on simulated data and also to the genome of a suspected HIV recombinant strain as well as to an investigation of recombination in the sequences of 15 laboratory mouse strains sequenced by Perlegen Sciences. Our findings indicate that our method allows us to distinguish between rate heterogeneity and variation in phylogeny caused by recombination without being restricted to 4-taxa data.

Unlabelled: Current genotyping algorithms typically call genotypes by clustering allele-specific intensity data on a single nucleotide polymorphism (SNP) by SNP basis. This approach assumes the availability of a large number of control samples that have been sampled on the same array and platform. We have developed a SNP genotyping algorithm for the Illumina Infinium SNP genotyping assay that is entirely within-sample and does not require the need for a population of control samples nor parameters derived from such a population. Our algorithm exhibits high concordance with current methods and >99% call accuracy on HapMap samples. The ability to call genotypes using only within-sample information makes the method computationally light and practical for studies involving small sample sizes and provides a valuable independent quality control metric for other population-based approaches., Availability: http://www.stats.ox.ac.uk/~giannoul/GenoSNP/.

Genome-wide single nucleotide polymorphism (SNP) genotyping platforms have made an important contribution to population genetics and genetic epidemiology. Recently there has been a realisation that these SNP platforms can also be used for typing copy number variants (CNVs). This allows for 'generalised' genotyping of both SNPs and CNVs simultaneously on a common sample set, with advantages in terms of cost and unified analysis. In this article we review various statistical approaches to calling CNVs from SNP data. We highlight three tiers of algorithms depending on the level of information used., (Copyright 2009 S. Karger AG, Basel.)

Array-based technologies have been used to detect chromosomal copy number changes (aneuploidies) in the human genome. Recent studies identified numerous copy number variants (CNV) and some are common polymorphisms that may contribute to disease susceptibility. We developed, and experimentally validated, a novel computational framework (QuantiSNP) for detecting regions of copy number variation from BeadArray SNP genotyping data using an Objective Bayes Hidden-Markov Model (OB-HMM). Objective Bayes measures are used to set certain hyperparameters in the priors using a novel re-sampling framework to calibrate the model to a fixed Type I (false positive) error rate. Other parameters are set via maximum marginal likelihood to prior training data of known structure. QuantiSNP provides probabilistic quantification of state classifications and significantly improves the accuracy of segmental aneuploidy identification and mapping, relative to existing analytical tools (Beadstudio, Illumina), as demonstrated by validation of breakpoint boundaries. QuantiSNP identified both novel and validated CNVs. QuantiSNP was developed using BeadArray SNP data but it can be adapted to other platforms and we believe that the OB-HMM framework has widespread applicability in genomic research. In conclusion, QuantiSNP is a novel algorithm for high-resolution CNV/aneuploidy detection with application to clinical genetics, cancer and disease association studies.

We present a method for Bayesian model-based hierarchical coclustering of gene expression data and use it to study the temporal transcription responses of an Anopheles gambiae cell line upon challenge with multiple microbial elicitors. The method fits statistical regression models to the gene expression time series for each experiment and performs coclustering on the genes by optimizing a joint probability model, characterizing gene coregulation between multiple experiments. We compute the model using a two-stage Expectation-Maximization-type algorithm, first fixing the cross-experiment covariance structure and using efficient Bayesian hierarchical clustering to obtain a locally optimal clustering of the gene expression profiles and then, conditional on that clustering, carrying out Bayesian inference on the cross-experiment covariance using Markov chain Monte Carlo simulation to obtain an expectation. For the problem of model choice, we use a cross-validatory approach to decide between individual experiment modeling and varying levels of coclustering. Our method successfully generates tightly coregulated clusters of genes that are implicated in related processes and therefore can be used for analysis of global transcript responses to various stimuli and prediction of gene functions.

We introduce a procedure for generalized monotonic curve fitting that is based on a Bayesian analysis of the isotonic regression model. Conventional isotonic regression fits monotonically increasing step functions to data. In our approach we treat the number and location of the steps as random. For each step level we adopt the conjugate prior to the sampling distribution of the data as if the curve was unconstrained. We then propose to use Markov chain Monte Carlo simulation to draw samples from the unconstrained model space and retain only those samples for which the monotonic constraint holds. The proportion of the samples collected for which the constraint holds can be used to provide a value for the weight of evidence in terms of Bayes factors for monotonicity given the data. Using the samples, probability statements can be made about other quantities of interest such as the number of change points in the data and posterior distributions on the location of the change points can be provided. The method is illustrated throughout by a reanalysis of the leukaemia data studied by Schell and Singh., (Copyright 2003 John Wiley & Sons, Ltd.)

This paper presents a Bayesian nonlinear approach for the analysis of spatial count data. It extends the Bayesian partition methodology of Holmes, Denison, and Mallick (1999, Bayesian partitioning for classification and regression, Technical Report, Imperial College, London) to handle data that involve counts. A demonstration involving incidence rates of leukemia in New York state is used to highlight the methodology. The model allows us to make probability statements on the incidence rates around point sources without making any parametric assumptions about the nature of the influence between the sources and the surrounding location.

Radial wavelet networks have recently been proposed as a method for nonparametric regression. In this paper we analyze their performance within a Bayesian framework. We derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model. This process bypasses the need to test or select a finite number of networks during the modeling process. Predictions are formed by mixing over many models of varying dimension and parameterization.We show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series.

Chitosan, the deacetylated form of chitin, is extracted from the shells of crustaceans. The strong positive charge carried by the chitosan molecule causes it to bind negatively charged substrates such as lipids. Orally administered chitosan binds fat in the intestine, blocking absorption, and has been shown to lower blood cholesterol in animals and humans. As a result it has been proposed that dietary supplementation with chitosan may inhibit the formation of atherosclerotic plaque. We have tested this hypothesis using the apolipoprotein E-deficient mouse model of atherosclerosis. This hypercholesterolaemic animal develops atherosclerosis without the need for dietary or surgical intervention. The apolipoprotein E-deficient mouse therefore provides an ideal model in which to study the effects of dietary chitosan on both blood cholesterol and atherosclerosis. Animals were fed for 20 weeks on a diet containing 5% chitosan or on a control diet. Blood cholesterol levels were significantly lower in the chitosan fed animals throughout the study, and at 20 weeks were 64% of control levels. When the area of aortic plaque in the two groups was compared a highly significant inhibition of atherogenesis, in both the whole aorta and the aortic arch, was observed in the chitosan fed animals--42 and 50%, respectively. Body growth was significantly greater in the chitosan fed animals. This study is the first to show a direct correlation between lowering of serum cholesterol with chitosan and inhibition of atherogenesis, and suggests that the agent could be used to inhibit the development of atherosclerosis in individuals with hypercholesterolaemia.